On bounds for the concentration function. 1
Structure theory of set addition, Astérisque, no. 258 (1999), pp. 425-436. 
@incollection{AST_1999__258__425_0,
     author = {Deshouillers, Jean-Marc and Freiman, Gregory A. and Yudin, Alexander A.},
     title = {On bounds for the concentration function. 1},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     pages = {425--436},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     year = {1999},
     mrnumber = {1701213},
     zbl = {0944.60028},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1999__258__425_0/}
}
TY  - CHAP
AU  - Deshouillers, Jean-Marc
AU  - Freiman, Gregory A.
AU  - Yudin, Alexander A.
TI  - On bounds for the concentration function. 1
BT  - Structure theory of set addition
AU  - Collectif
ED  - Deshouilliers Jean-Marc
ED  - Landreau Bernard
ED  - Yudin Alexander A.
T3  - Astérisque
PY  - 1999
SP  - 425
EP  - 436
IS  - 258
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1999__258__425_0/
LA  - en
ID  - AST_1999__258__425_0
ER  - 
%0 Book Section
%A Deshouillers, Jean-Marc
%A Freiman, Gregory A.
%A Yudin, Alexander A.
%T On bounds for the concentration function. 1
%B Structure theory of set addition
%A Collectif
%E Deshouilliers Jean-Marc
%E Landreau Bernard
%E Yudin Alexander A.
%S Astérisque
%D 1999
%P 425-436
%N 258
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_1999__258__425_0/
%G en
%F AST_1999__258__425_0
Deshouillers, Jean-Marc; Freiman, Gregory A.; Yudin, Alexander A. On bounds for the concentration function. 1, dans Structure theory of set addition, Astérisque, no. 258 (1999), pp. 425-436. http://archive.numdam.org/item/AST_1999__258__425_0/

[1] Arak T. V. and Zaitsev A. Yu., Uniform limit theorems for sums of independent random variables, Proceedings of the Steklov Institute of Mathematics, issue 1, 1988, 41-61. | MR | Zbl

[2] Doeblin W. and Lévy P., Sur les sommes de variables aléatoires indépendantes à dispersions bornées inférieurement, CR. Acad. Sci. Paris 202, 1936, 2027-2029. | JFM

[3] Esséen C. G., On the Kolmorogov-Rogozin inequality for the concentration function, Z. Wahrscheinlichkeitstheorie und verw. Gebiete, 5, 1966, 210-216. | DOI | MR | Zbl

[4] Freiman G. A., Moskvin D. A. and A.A. Yudin A. A., Inverse problems of additive number theory and local limit theorems for lattice random variables, (in Russian), Number theoretic studies in the Markov spectrum and in the structure theory of set addition, Kalinin Gos. Univ., Moscow, 1973, 148-162. | MR | Zbl

[5] Kesten H., A sharper form of the Doeblin-Levy-Kolmogorov-Rogozin inequality for concentration functions, Math. Scand. 25, 1969, 133-144. | DOI | EuDML | MR | Zbl

[6] Kolmogorov A. N., Sur les propriétés des functions de concentration de M. P. Lévy, Ann. Inst. H. Poincaré 16, 1958-1960, 27-34. | EuDML | Numdam | MR | Zbl

[7] Ledoux M. and Talagrand M. Probability in Banach spaces. Isoperimetry and processes, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 23, Springer-Verlag, Berlin, 1991, xii+480 pp. ISBN: 3-540-52013-9. | MR | Zbl

[8] Mann H. B., The Addition Theorems of Groups Theory and Number Theory, Interscience, 18, J. Wiley, New York, 1965. | MR | Zbl

[9] Petrov V. V., Limit theorems for sums of independent random variables, (Russian), Probability Theory and Mathematical Statistics, "Nauka", Moscow, 1987, 318 pp. | MR | Zbl

[10] Postnikova L. P. and Yudin A. A., On the concentration function, Th. Probability Appl., 22, 1977, 302-305. | MR | Zbl

[11] Postnikova L. P. and Yudin A. A., An analytic method for estimates of the concentration function, Proc. Steklov Inst. Math., 1980, 153-161. | Zbl

[12] Rogozin B. A., On the increase of dispersion of sums of independent random variables, Th. Probability Appl., 6, 1961, 97-99. | DOI | MR | Zbl